As a physiological phenomenon, sleep takes up approximately 30% of human life and significantly affects people’s quality of life. To assess the quality of night sleep, polysomnography (PSG) has been recognized as the gold standard for sleep staging. The drawbacks of such a clinical device, however, are obvious, since PSG limits the patient’s mobility during the night, which is inconvenient for in-home monitoring. In this paper, a noncontact vital signs monitoring system using the piezoelectric sensors is deployed. Using the so-designed noncontact sensing system, heartbeat interval (HI), respiratory interval (RI), and body movements (BM) are separated and recorded, from which a new dimension of vital signs, referred to as the coordination of heartbeat interval and respiratory interval (CHR), is obtained. By extracting both the independent features of HI, RI, and BM and the coordinated features of CHR in different timescales, Wake-REM-NREM sleep staging is performed, and a postprocessing of staging fusion algorithm is proposed to refine the accuracy of classification. A total of 17 all-night recordings of noncontact measurement simultaneous with PSG from 10 healthy subjects were examined, and the leave-one-out cross-validation was adopted to assess the performance of Wake-REM-NREM sleep staging. Taking the gold standard of PSG as reference, numerical results show that the proposed sleep staging achieves an averaged accuracy and Cohen’s Kappa index of 82.42% and 0.63, respectively, and performs robust to subjects suffering from sleep-disordered breathing.